Question 178191
{{{-9-3m-m<9m-9}}} Start with the given inequality.



{{{-4m-9<9m-9}}} Combine like terms on the left side.



{{{-4m<9m-9+9}}} Add {{{9}}} to both sides.



{{{-4m-9m<-9+9}}} Subtract {{{9m}}} from both sides.



{{{-13m<-9+9}}} Combine like terms on the left side.



{{{-13m<0}}} Combine like terms on the right side.



{{{m>(0)/(-13)}}} Divide both sides by {{{-13}}} to isolate {{{m}}}. note: Remember, the inequality sign flips when we divide both sides by a negative number. 



{{{m>0}}} Reduce.



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Answer:


So the answer is {{{m>0}}} 



So the answer in interval notation is *[Tex \LARGE \left(0,\infty\right)]



Also, the answer in set-builder notation is  *[Tex \LARGE \left\{m\|m>0\right\}]



Here's the graph of the solution set on the number line:


{{{drawing(500,80,-10, 10,-10, 10,
number_line( 500, -10, 10),

arrow(0,0,10,0),
arrow(0,0.30,10,0.30),
arrow(0,0.15,10,0.15),
arrow(0,-0.15,10,-0.15),
arrow(0,-0.30,10,-0.30),

circle(0,0,0.3),
circle(0,0,0.3),
circle(0,0,0.3),
circle(0,0,0.3-0.02)
)}}} Graph of the solution set where there is an open circle at the endpoint {{{m=0}}}